Explain the working of a simple microscope and show that its angular magnification is given by $M=1+\left(\raisebox{1ex}{${\displaystyle D}$}\!\left/ \!\raisebox{-1ex}{$f$}\right.\right)$, where $D$ is the least distance of distinct vision.

Draw a labelled ray-diagram for a simple microscope (magnifying glass) and deduce an expression for its angular magnification in normal use.

Draw a neat labelled ray diagram showing the formation of an image at the least distance of distinct vision $D$ by a simple microscope. When the final image is at $D$, derive an expression for its magnifying power at $D$.

Draw a labelled ray-diagram of an image formed by a compound microscope when the final image lies at least distance of distinct vision. Write any one expression for its magnifying power. Why is its objective of a very small aperture?

With the help of a labelled diagram, explain the construction and working of a compound microscope. Derive an expression for its magnifying power. How can the magnifying power be increased?

Draw a ray-diagram of an astronomical telescope and derive an expression for its magnifying power when the image is formed at infinity.

Draw a labelled ray diagram of an image formed by a refracting telescope with final image formed at infinity Derive an expression for its magnifying power with the final image at infinity.

Draw the ray-diagram for the formation of image by a refracting telescope having the final image formed at infinity Define the angular magnification and derive the formula for the same for image formed at infinity.